arXiv subjects

Chun-Xiao Liu

Publications and source records attributed to Chun-Xiao Liu.

At least 37 records · Page 2Linked to original sources

arXiv2023

Singlet and triplet Cooper pair splitting in hybrid superconducting nanowires

In most naturally occurring superconductors, electrons with opposite spins are paired up to form Cooper pairs. This includes both conventional $s$-wave superconductors such as aluminum as well as high-$T_\text{c}$, $d$-wave superconductors. Materials with intrinsic $p$-wave superconductivity, hosting Cooper pairs made of equal-spin electrons, have not been conclusively identified, nor synthesized, despite promising progress. Instead, engineered platforms where $s$-wave superconductors are brought into contact with magnetic materials have shown convincing signatures of equal-spin pairing. Here, we directly measure equal-spin pairing between spin-polarized quantum dots. This pairing is proximity-induced from an $s$-wave superconductor into a semiconducting nanowire with strong spin-orbit interaction. We demonstrate such pairing by showing that breaking a Cooper pair can result in two electrons with equal spin polarization. Our results demonstrate controllable detection of singlet and triplet pairing between the quantum dots. Achieving such triplet pairing in a sequence of quantum dots will be required for realizing an artificial Kitaev chain.

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arXiv2022

Tunable superconducting coupling of quantum dots via Andreev bound states in semiconductor-superconductor nanowires

Semiconductor quantum dots have proven to be a useful platform for quantum simulation in the solid state. However, implementing a superconducting coupling between quantum dots mediated by a Cooper pair has so far suffered from limited tunability and strong suppression. This has limited applications such as Cooper pair splitting and quantum dot simulation of topological Kitaev chains. In this work, we propose how to mediate tunable effective couplings via Andreev bound states in a semiconductor-superconductor nanowire connecting two quantum dots. We show that in this way it is possible to individually control both the coupling mediated by Cooper pairs and by single electrons by changing the properties of the Andreev bound states with easily accessible experimental parameters. In addition, the problem of coupling suppression is greatly mitigated. We also propose how to experimentally extract the coupling strengths from resonant current in a three-terminal junction. Our proposal will enable future experiments that have not been possible so far.

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arXiv2022

Controlled crossed Andreev reflection and elastic co-tunneling mediated by Andreev bound states

A short superconducting segment can couple attached quantum dots via elastic co-tunneling (ECT) and crossed Andreev reflection (CAR). Such coupled quantum dots can host Majorana bound states provided that the ratio between CAR and ECT can be controlled. Metallic superconductors have so far been shown to mediate such tunneling phenomena, albeit with limited tunability. Here we show that Andreev bound states formed in semiconductor-superconductor heterostructures can mediate CAR and ECT over mesoscopic length scales. Andreev bound states possess both an electron and a hole component, giving rise to an intricate interference phenomenon that allows us to tune the ratio between CAR and ECT deterministically. We further show that the combination of intrinsic spin-orbit coupling in InSb nanowires and an applied magnetic field provides another efficient knob to tune the ratio between ECT and CAR and optimize the amount of coupling between neighboring quantum dots.

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arXiv2022

Impact of disorder on the distribution of gate coupling strengths in a spin qubit device

A scalable spin-based quantum processor requires a suitable semiconductor heterostructure and a gate design, with multiple alternatives being investigated. Characterizing such devices experimentally is a demanding task, with the full development cycle taking at least months. While numerical simulations are more time-efficient, their predictive power is limited due to unavoidable disorder and device-to-device variation. We develop a spin-qubit device simulation for determining the distribution of the coupling strengths between the electrostatic gate potentials and the effective device Hamiltonian in presence of disorder. By comparing our simulation results with the experimental data, we demonstrate that the coupling of the gate voltages to the dot chemical potential and the interdot tunnel coupling match up to disorder-induced variance. To demonstrate the flexibility of our approach, we also analyze an alternative non-planar geometry inspired by FinFET devices.

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arXiv2022

Mechanisms of Andreev reflection in quantum Hall graphene

We simulate a hybrid superconductor-graphene device in the quantum Hall regime to identify the origin of downstream resistance oscillations in a recent experiment [Zhao et. al. Nature Physics 16, (2020)]. In addition to the previously studied Mach-Zehnder interference between the valley-polarized edge states, we consider disorder-induced scattering, and the previously overlooked appearance of the counter-propagating states generated by the interface density mismatch. Comparing our results with the experiment, we conclude that the observed oscillations are induced by the interfacial disorder, and that lattice-matched superconductors are necessary to observe the alternative ballistic effects.

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arXiv2022

Optimizing the topological properties of stacking semiconductor-ferromagnet-superconductor heterostructures

We study the electronic properties of a planar semiconductor-superconductor heterostructure, in which a thin ferromagnetic insulator layer lies in between and acts as a spin filtering barrier. We find that in such a system one can simultaneously enhance the strengths of all the three important induced physical quantities, i.e., Rashba spin-orbit coupling, exchange coupling, and superconducting pairing potential, for the hybrid mode by external gating. Our results show specific advantage of this stacked device geometry compared to conventional devices. We further discuss how to optimize geometrical parameters for the heterostructure and complement our numerical simulations with analytic calculations.

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arXiv2021

Quantized and unquantized zero-bias tunneling conductance peaks in Majorana nanowires: Conductance below and above $ 2e^2/h $

Majorana zero modes can appear at the wire ends of a 1D topological superconductor and manifest themselves as a quantized zero-bias conductance peak in the tunneling spectroscopy of normal-superconductor junctions. However, in superconductor-semiconductor hybrid nanowires, zero-bias conductance peaks may arise owing to topologically trivial mechanisms as well, mimicking the Majorana-induced topological peak in many aspects. In this work, we systematically investigate the characteristics of zero-bias conductance peaks for topological Majorana bound states, trivial quasi-Majorana bound states and low-energy Andreev bound states arising from smooth potential variations, and disorder-induced subgap bound states. Our focus is on the conductance peak value (i.e., equal to, greater than, or less than $2e^2/h$), as well as the robustness (plateau- or spike-like) against the tuning parameters (e.g., the magnetic field and tunneling gate voltage) for zero-bias peaks arising from the different mechanisms. We find that for Majoranas and quasi-Majoranas, the zero-bias peak values are no more than $2e^2/h$, and a quantized conductance plateau forms generically as a function of parameters. By contrast, for conductance peaks due to low-energy Andreev bound states or disorder-induced bound states, the peak values may exceed $2e^2/h$, and a conductance plateau is rarely observed unless through careful postselection and fine-tuning. Our findings should shed light on the interpretation of experimental measurements on the tunneling spectroscopy of normal-superconductor junctions of hybrid Majorana nanowires.

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arXiv2021

Josephson current via an isolated Majorana zero mode

We study the equilibrium dc Josephson current in a junction between an $s$-wave and a topological superconductor. Cooper pairs from the $s$-wave superconducting lead can transfer to the topological side either via an unpaired Majorana zero mode localized near the junction, or via the above-gap continuum states. We find that the Majorana contribution to the supercurrent can be switched on when time-reversal symmetry in the conventional lead is broken, e.g., by an externally applied magnetic field inducing a Zeeman splitting. Moreover, if the magnetic field has a component in the direction of the effective spin-orbit field, there will be a Majorana-induced anomalous supercurrent at zero phase difference. This behavior may serve as a signature characteristic of Majorana zero modes, and is accessible to devices with only superconducting contacts.

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arXiv2021

Large zero-bias peaks in InSb-Al hybrid semiconductor-superconductor nanowire devices

We report electron transport studies on InSb-Al hybrid semiconductor-superconductor nanowire devices. Tunnelling spectroscopy is used to measure the evolution of subgap states while varying magnetic field and voltages applied to various nearby gates. At magnetic fields between 0.7 and 0.9 T, the differential conductance contains large zero bias peaks (ZBPs) whose height reaches values on the order 2e2/h. We investigate these ZBPs for large ranges of gate voltages in different devices. We discuss possible interpretations in terms of disorder-induced subgap states, Andreev bound states and Majorana zero modes.

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arXiv2021

Conductance asymmetries in mesoscopic superconducting devices due to finite bias

Tunneling conductance spectroscopy in normal metal-superconductor junctions is an important tool for probing Andreev bound states in mesoscopic superconducting devices, such as Majorana nanowires. In an ideal superconducting device, the subgap conductance obeys specific symmetry relations, due to particle-hole symmetry and unitarity of the scattering matrix. However, experimental data often exhibits deviations from these symmetries or even their explicit breakdown. In this work, we identify a mechanism that leads to conductance asymmetries without quasiparticle poisoning. In particular, we investigate the effects of finite bias and include the voltage dependence in the tunnel barrier transparency, finding significant conductance asymmetries for realistic device parameters. It is important to identify the physical origin of conductance asymmetries: in contrast to other possible mechanisms such as quasiparticle poisoning, finite-bias effects are not detrimental to the performance of a topological qubit. To that end we identify features that can be used to experimentally determine whether finite-bias effects are the source of conductance asymmetries.

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arXiv2020

Electronic properties of InAs/EuS/Al hybrid nanowires

We study the electronic properties of InAs/EuS/Al heterostructures as explored in a recent experiment [S. Vaitiekenas \emph{et al.}, Nat. Phys. (2020)], combining both spectroscopic results and microscopic device simulations. In particular, we use angle-resolved photoemission spectroscopy to investigate the band bending at the InAs/EuS interface. The resulting band offset value serves as an essential input to subsequent microscopic device simulations, allowing us to map the electronic wave function distribution. We conclude that the magnetic proximity effects at the Al/EuS as well as the InAs/EuS interfaces are both essential to achieve topological superconductivity at zero applied magnetic field. Mapping the topological phase diagram as a function of gate voltages and proximity-induced exchange couplings, we show that the ferromagnetic hybrid nanowire with overlapping Al and EuS layers can become a topological superconductor within realistic parameter regimes, and that the topological phase can be optimized by external gating. Our work highlights the need for a combined experimental and theoretical effort for faithful device simulation.

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arXiv2019

Protocol for reading out Majorana vortex qubit and testing non-Abelian statistics

The successful test of non-Abelian statistics not only serves as a milestone in fundamental physics but also provides a quantum gate operation in topological quantum computation. An accurate and efficient readout scheme of a topological qubit is an essential step toward the experimental confirmation of non-Abelian statistics. In the current work, we propose a protocol to read out the quantum state of a Majorana vortex qubit on a topological superconductor island. The protocol consists of four Majorana zero modes trapped in spatially well-separated vortex cores on the two-dimensional surface of a Coulomb blockaded topological superconductor. Our proposed measurement is implemented by a pair of weakly coupled Majorana modes separately in touch with two normal metal leads, and the readout is realized by observing the conductance peak location in terms of gate voltage. Using this protocol, we can further test the non-Abelian statistics of Majorana zero modes in the two-dimensional platform. A successful readout of Majorana qubit is a crucial step towards the future application of topological quantum computation. In addition, this Coulomb blockaded setup can distinguish Majorana zero modes from Caroli-de Gennes-Matricon modes in vortex cores.

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arXiv2019

Proposal for measuring the parity anomaly in a topological superconductor ring

A topological superconductor ring is uniquely characterized by a switch in the ground state fermion number parity upon insertion of one superconducting flux quantum - a direct consequence of the topological `parity anomaly.' Despite the many other tantalizing signatures and applications of topological superconductors, this fundamental, defining property remains to be observed experimentally. Here we propose definitive detection of the fermion parity switch from the charging energy, temperature, and tunnel barrier dependence of the flux periodicity of two-terminal conductance of a floating superconductor ring. We extend the Ambegaokar-Eckern-Sch{ö}n formalism for superconductors with a Coulomb charging energy to establish new explicit relationships between thermodynamic and transport properties of such a ring and the topological invariant of the superconductor. Crucially, we show that the topological contribution to the conductance oscillations can be isolated from Aharonov-Bohm oscillations of non-topological origin by their different dependence on the charging energy or barrier transparency.

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arXiv2019

Conductance feature smearing and anisotropic suppression of induced superconductivity in a Majorana nanowire

In a recent high-quality experimental work on normal metal--superconducting nanowire junctions arXiv:1807.01940 (2018), strong anisotropic suppression of induced superconductivity has been observed in tunnel conductance measurements in the presence of applied magnetic field with variable orientation. Following this finding, we investigate theoretically the dependence of tunnel conductance on the direction of the Zeeman field in order to understand the operational mechanisms and to extract effective system parameters. Second, motivated by a generic discrepancy between experiment and theory, i.e., many in-gap and above-gap conductance features predicted by theory are barely observed in experiments, we study several mechanisms possibly responsible for the suppression of the theoretically predicted conductance features (e.g., length of the nanowire, self-energy effect due to the proximity effect, finite temperature, finite dissipation, and multiband effect). One essential finding in the current work is that only by a combined understanding of both suppression mechanisms can we extract effective system parameters from the experimental data (e.g., the effective nanowire-superconductor coupling, the effective Landé $g$ factor, and the chemical potential of the semiconducting nanowire). In addition, we consider topologically trivial Andreev bound states in hybrid nanowires in the presence of potential inhomogeneities, such as external quantum dots or potential inhomogeneities inside the nanowire. We compare the anisotropic, field-dependent features induced by these nontopological Andreev bound states with the corresponding features produced by topological Majorana zero modes in pristine nanostructures, so that we can provide guidance to differentiate between the topologically trivial and nontrivial cases.

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arXiv2018

Metamorphosis of Andreev bound states into Majorana bound states in pristine nanowires

We show theoretically that in the generic finite chemical potential situation, the clean superconducting spin-orbit-coupled nanowire has two distinct nontopological regimes as a function of Zeeman splitting (below the topological quantum phase transition): one is characterized by finite-energy in-gap Andreev bound states, while the other has only extended bulk states. The Andreev bound state regime is characterized by strong features in the tunneling spectra creating a "gap closure" signature, but no "gap reopening" signature should be apparent above the topological quantum phase transition, in agreement with most recent experimental observations. The gap closure feature is actually the coming together of the Andreev bound states at high chemical potential rather than a simple trivial gap of extended bulk states closing at the transition. Our theoretical finding establishes the generic intrinsic Andreev bound states on the trivial side of the topological quantum phase transition as the main contributors to the tunneling conductance spectra, providing a generic interpretation of existing experiments in clean Majorana nanowires. Our work also explains why experimental tunnel conductance spectra generically have gap closing features below the topological quantum phase transition, but no gap opening features above it.

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arXiv2018

Distinguishing topological Majorana bound states from trivial Andreev bound states: Proposed tests through differential tunneling conductance spectroscopy

Trivial Andreev bound states arising from chemical potential variations could lead to zero-bias tunneling conductance peaks at finite magnetic fields in class $D$ nanowires, precisely mimicking the predicted zero-bias conductance peaks arising from the topological Majorana bound states. This finding raises a serious question on the efficacy of using zero-bias tunneling conductance peaks, by themselves, as evidence supporting the existence of topological Majorana bound states in nanowires. In the current work, we provide specific experimental protocols for tunneling spectroscopy measure- ments to distinguish between Andreev and Majorana bound states without invoking more demand- ing nonlocal measurements which have not yet been successfully performed in nanowire systems. In particular, we discuss three distinct experimental schemes involving response of the zero-bias peak to local perturbations of the tunnel barrier, overlap of bound states from the wire ends, and most compellingly, introducing a sharp localized potential in the wire itself to perturb the zero-bias tun- neling peaks. We provide extensive numerical simulations clarifying and supporting our theoretical predictions.

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arXiv2017

Electron temperature and tunnel coupling dependence of zero-bias and almost-zero-bias conductance peaks in Majorana nanowires

A one-dimensional semiconductor nanowire proximitized by a nearby superconductor may become a topological superconductor hosting localized Majorana zero modes at the two wire ends in the presence of spin-orbit coupling and Zeeman spin splitting (arising from an external magnetic field). The hallmark of the presence of such Majorana zero modes is the appearance of a zero-temperature quantized zero-bias conductance peak in the tunneling spectroscopy of the Majorana nanowire. We theoretically study the temperature and the tunnel coupling dependence of the tunneling conductance in such nanowires to understand possible intrinsic deviations from the predicted conductance quantization. We find that the full temperature and the tunneling transmission dependence of the tunnel conductance does not obey any simple scaling relation, and estimating the zero-temperature conductance from finite-temperature and finite-tunnel-broadening tunneling data is difficult in general. A scaling relation, however, does hold at the extreme weak-tunneling low-temperature limit where the conductance depends only on the dimensionless ratio of the temperature and tunnel broadening. We also consider the tunneling contributions from nontopological Andreev bound states which may produce almost-zero-bias conductance peaks, which are not easy to distinguish from the Majorana-induced zero-bias peaks, finding that the nontopological almost-zero-modes associated with Andreev bound states manifest similar temperature and transmission dependence as the topological Majorana modes. We comment on the Zeeman splitting dependence of the zero-bias conductance peak for finite temperature and tunnel coupling.

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arXiv2017

Quantized Majorana conductance

Majorana zero-modes hold great promise for topological quantum computing. Tunnelling spectroscopy in electrical transport is the primary tool to identify the presence of Majorana zero-modes, for instance as a zero-bias peak (ZBP) in differential-conductance. The Majorana ZBP-height is predicted to be quantized at the universal conductance value of 2e2/h at zero temperature. Interestingly, this quantization is a direct consequence of the famous Majorana symmetry, 'particle equals antiparticle'. The Majorana symmetry protects the quantization against disorder, interactions, and variations in the tunnel coupling. Previous experiments, however, have shown ZBPs much smaller than 2e2/h, with a recent observation of a peak-height close to 2e2/h. Here, we report a quantized conductance plateau at 2e2/h in the zero-bias conductance measured in InSb semiconductor nanowires covered with an Al superconducting shell. Our ZBP-height remains constant despite changing parameters such as the magnetic field and tunnel coupling, i.e. a quantized conductance plateau. We distinguish this quantized Majorana peak from possible non-Majorana origins, by investigating its robustness on electric and magnetic fields as well as its temperature dependence. The observation of a quantized conductance plateau strongly supports the existence of non-Abelian Majorana zero-modes in the system, consequently paving the way for future braiding experiments.

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